Feature Selection Based on Structured Sparsity: A Comprehensive Study

Feature selection (FS) is an important component of many pattern recognition tasks. In these tasks, one is often confronted with very high-dimensional data. FS algorithms are designed to identify the relevant feature subset from the original features, which can facilitate subsequent analysis, such as clustering and classification. Structured sparsity-inducing feature selection (SSFS) methods have been widely studied in the last few years, and a number of algorithms have been proposed. However, there is no comprehensive study concerning the connections between different SSFS methods, and how they have evolved. In this paper, we attempt to provide a survey on various SSFS methods, including their motivations and mathematical representations. We then explore the relationship among different formulations and propose a taxonomy to elucidate their evolution. We group the existing SSFS methods into two categories, i.e., vector-based feature selection (feature selection based on lasso) and matrix-based feature selection (feature selection based on l_r,p-norm). Furthermore, FS has been combined with other machine learning algorithms for specific applications, such as multitask learning, multilabel learning, multiview learning, classification, and clustering. This paper not only compares the differences and commonalities of these methods based on regression and regularization strategies, but also provides useful guidelines to practitioners working in related fields to guide them how to do feature selection.